Abstract
The tunneling problem of degenerate classical ground states is discussed by using the WKB wave function for systems with many degrees of freedom. The method is elaborated for a simple multi-dimensional potential system with two absolute minima. The WKB wave function is constructed for the forbidden region of configuration space by using imaginary time (Euclidean) solutions of classical equations of motion. This imaginary time is used as a geometrical parameter of phase space and is not related to the true time of the problem, which is eliminated by studying stationary-state wave functions. The matching of the WKB wave function to the harmonic oscillator wave function in the allowed region is discussed to obtain the ground state energy. The result is compared with the imaginary time path integral computation. The agreement between the two results follows from scattering theory applied to the small fluctuation equation.
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